2010 Cayley Problem 24

A coin that is 8 cm in diameter is tossed onto a 5 by 5 grid of squares each having side length 10 cm. A coin is in a winning position if no part of it touches or crosses a grid line, otherwise it is in a losing position. Given that the coin lands in a random position so that no part of it is off the grid, what is the probability that it is in a winning position?

\textbf{(A)}\ \frac{25}{441}\quad \textbf{(B)}\ \frac{1}{25}\quad \textbf{(C)}\ \frac{1}{49}\quad \textbf{(D)}\ \frac{5}{147}\quad \textbf{(E)}\ \frac{4\pi}{25}

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.